WILCOX TEST Meaning and
Definition
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The Wilcox Test, also known as the Wilcoxon Signed-Rank Test, is a statistical non-parametric test used to determine if there is a significant difference between paired or related samples. Typically employed when the data do not adhere to the assumptions required for a parametric test, it is particularly helpful for small sample sizes or when the data is not normally distributed.
The Wilcox Test assesses whether the median of the differences between the paired observations differs significantly from zero. It accomplishes this by ranking the absolute values of the differences and then summing the ranks. Unlike parametric tests, the Wilcox Test does not rely on assumptions about the underlying distribution of the data, making it robust against outliers or non-normal distributions.
To conduct a Wilcox Test, the null hypothesis assumes that the median difference between the paired observations is zero, while the alternative hypothesis posits that the median difference is not zero. The test statistic used in the Wilcox Test is the sum of the ranks of the positive or negative differences, based on whether the alternative hypothesis is one-sided or two-sided, respectively.
The Wilcox Test produces a p-value, which measures the probability of obtaining the observed results, or results more extreme, if the null hypothesis were true. A small p-value indicates evidence against the null hypothesis, suggesting a significant difference between the paired samples. Conversely, a large p-value suggests that the null hypothesis cannot be rejected, indicating no significant difference.
In summary, the Wilcox Test is a flexible and robust statistical procedure used to analyze related samples or paired observations, contrasting their medians without reliance on the underlying distribution of the data.
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Etymology of WILCOX TEST
The term "Wilcoxon test" or "Wilcoxon rank-sum test" is named after Frank Wilcoxon, an American mathematician and engineer. Frank Wilcoxon developed this non-parametric statistical test in 1945 as an alternative to the t-test when the assumptions of the t-test are violated. The test is used to compare the distribution of two samples to determine whether one sample tends to have larger values than the other. The name "Wilcoxon test" honors the person who introduced and developed it.
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